@article{article_441621, title={Hypergroups and their pullback and pushout structures}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={47}, pages={237–250}, year={2018}, author={Alp, Murat and Davvaz, Bijan}, keywords={Action,Crossed module,Hypergroup,Fundamental relation,Pull- back,Pushout}, abstract={<p> <span style="float:none;background-color:rgb(255,255,255);color:rgb(0,0,0);font-family:’Helvetica Neue’, Helvetica, Arial, sans-serif;font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;">Hypergroups in the sense of Marty are very important and a rather </span> <span style="float:none;background-color:rgb(255,255,255);color:rgb(0,0,0);font-family:’Helvetica Neue’, Helvetica, Arial, sans-serif;font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;">difficult subject to be understood since they do not generally have any identity or inverse element. Crossed modules are one of the most im </span> <span style="float:none;background-color:rgb(255,255,255);color:rgb(0,0,0);font-family:’Helvetica Neue’, Helvetica, Arial, sans-serif;font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;">portant tools to be applied on groups. In this study, we combine hypergroups and crossed modules to obtain the crossed modules of the </span> <span style="float:none;background-color:rgb(255,255,255);color:rgb(0,0,0);font-family:’Helvetica Neue’, Helvetica, Arial, sans-serif;font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;">hypergroups. We shortly present hypergroups with their properties and examples. In addition two important applications of crossed modules </span> <span style="float:none;background-color:rgb(255,255,255);color:rgb(0,0,0);font-family:’Helvetica Neue’, Helvetica, Arial, sans-serif;font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;">are given. These applications are about pullback and pushout crossed module of hypergroups and their properties. The denition of hypergroups generated by sets plays vital roles throughout the paper. </span> <br style="background-color:transparent;color:rgb(0,0,0);font-size:12.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;" /> <b> </b> <i> </i> <u> </u> <sub> </sub> <sup> </sup> <strike> </strike> <br /> </p>}, number={2}, publisher={Hacettepe University}